Dispersion on certain Cartesian products of graphs

Kaïs Ammari; Mostafa Sabri

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arXiv · 2208.10805

Dispersion on certain Cartesian products of graphs

Kaïs Ammari·Mostafa Sabri

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Abstract

In this short note we prove a sharp dispersive estimate $\|\mathrm{e}^{\mathrm{i} tH} f\|_\infty < t^{-d/3}\|f\|_1$ for any Cartesian product $\mathbb{Z}^d\mathop\square G_F$ of the integer lattice and a finite graph. This includes the infinite ladder, $k$-strips and infinite cylinders, which can be endowed with certain potentials.

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Kaïs Ammari, Mostafa Sabri. 2022-08-23. Dispersion on certain Cartesian products of graphs. https://arxiv.org/abs/2208.10805

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